My mom has a problem with my girlfriend?

My girlfriend is going with us to Disneyland tomorrow. My dad is perfectly fine with it and so was my mom. A close friend of my girlfriend died about a month ago and tomorrows his birthday so her mom is going to go with the mom of the kid who died to go and have a memorial and go to the cemetary and stuff. Since the mom will be out late, my girlfriend (who is 14, were the same age) if she could sleep over. I doubted it because my parents are very conservative. So early today i asked my dad "Dad is it ok if _____ sleeps over." It came to a surprise to him but after telling him that her mom would be with the mom having a memorial for her son, and her sister would be at her grandmas house who lives about 20 minutes away, he said he would have no problem with it, and that he trusts me, she would just have to sleep in the guest room. He said "Yes i have no problem, but check with your mom just to make sure." I wasnt thinking and without calling my mom i called her and i said, yes its fine you can sleep over, my parents are ok with it, youll just have to sleep in a different room. She made plans with her mom and her mom said yes she can stay over. Later that day i told my mom that dad said yes that she could stay over and she was very upset. She yelled "NO! I WILL NOT HAVE A GIRL IN THIS HOUSE!" Later my dad came back from the market and talked to her. My dad than asked why we couldnt drop her off where her mom would be, i said the mom is going to different places with the mom so they wont stay at home. And she cant stay home alone and her sister will be at her grandmas house. My mom ranted and ranted said that shell drive her whereever she needs to be as long as she doesnt sleep over. My dad than pulls the tables on me and says its my fault that i didnt tell my mom (i taught his approval was all i needed) so my mom said, fine she can sleep over, but im not gunna go to disneyland (almost like a little 4 year old brat) i than told her if it makes her feel bad i tell her that she cant sleep over. She said no no no. I feel bad for my girlfriend because i already told her it was ok, she already comfirmed with her mom, and now i feel bad because of how my mom is acting. A few minutes ago she came in to my room and she apologized. She said you can still go with your plans and ill go to disneyland with you. I dont want you to feel bad and just know im more mad at your dad, not at you. So now tomorrow morning my dad wants to talk with ______ mom just to make sure its good and she wants to know her. What should i do about this entire situation? Am i right, is my mom overreacting? Many guys have slept over, most of them are bad kids who smoke, do drugs and my mom is ok with it, it just cant be a girl. And my girlfriend is a really nice down to earth, straight A student, just the problem is that shes a girl. What do you guys think about the entire situation?